In Ref. [1]}, we provide a topological understanding of
the PHE in dielectrics with Raman spin-phonon coupling for the honeycomb
lattice structure. Because of the nature of phonons, the phonon Hall
conductivity, which is not directly proportional to the Chern number,
is not quantized. We observed a phase transition in the PHE, which
corresponds to the sudden change of band topology, characterized by
the altering of integer Chern numbers. Such PHE can be explained by
touching and splitting of phonon bands. To check whether the mechanism
of the PHE is universal, in the following we apply the theory to the
kagome lattice, which has been used to model many real materials
[2]}.
